We have,

ABCD is a rhombus with side 10 cm and diagonal BD=16 CM

We know that rhombus of diagonal bisects each other at 90

BO=OD=8cm

In AOB

AB²=AO²+BO²

10²= AO² +8²

100= AO²+64

AO²=100-64

AO²=36

AO=

AO=6 cm

∴ AC=AO+OC

AC=6+6

AC=12 cm